3.1 Graphing Simple Inequalities
After watching the video above on graphing, you need to match the inequality statements below in the document below with their corresponding graphs.
3.1 wikispace journal.doc
In your wikispace journal, explain your entire thought process (from your first match to your last) and how you narrowed down the choices and knew which graph matched which inequality statement.
Table with answers to the above document is in the document below
To narrow down my choices I looked at the sign of the inequality and determined whether the dot was open or closed then I looked at the point of the inequality which tells me which side to shade the line and I looked at the inequality that had "or" in it which told me that there where no solutions and when there was just and "x" there is solutions.
3.2 Summarize what we did in class today. Explain what similar features are shown in the graph x>5 as you would graph it on a number line and x>5 as you would graph it on a coordinate plane. Also explain the similarities of x<=3 as graphed on a number line and x<=3 on a coordinate plane. Explain how this same thinking applies to y<2x+1 ?? How do you know which side of the line should be shaded since the line is slanted? Be sure to explain the short-cut method as well as the algebraic method you could use to prove that the correct side of the line has been shaded.
x>5 on a number line would have an open circle over 5, going to the right. On a coordinate plane, x>5 would be a dotted line thats shaded above. The open circle on a number line represents a dotted line on a coordinate plane. X≤3 on a number line would have a closed circle above 3 going to the left. On a coordinate plane, x≤3 would have a solid line shaded below. The same thing go with y<2x+1, because is < which means that it will be a dashed line, and shaded below. If its > or ≥, the line is shaded above, and if it's < or ≤, the line is shaded below. To prove which side of the line that has to be shaded, you can pick a point on the coordinate plane from the shaded region, and plug the coordinates into the inequality.
3.3 (Looking at graph on page 113) Write the inequality whose graph is shown. Explain every step of your thinking and how you came up with the inequality.
y≤-1/2+4 First, i looked for the mx+b. I found that the Y intercept was 4, and the slope was -1/2, because it was going down to the right and up to the left. Then, i looked at the kind of line that was shown, and where the shading was. It was a solid line and was shaded below, which meant that it was ≤
3.4
Looking at the shaded graph in the document below, you need to identify a point that is a solution to the system and explain how you know it is a solution by looking at the graph. Also, identify a point that is a solution to only one of the inequalities, but NOT a solution to the system. Explain how you might test a point to determine whether it is a solution to the system or not?
3.4.doc A point that is a solution to the system is (-6,6) I know its a solution by looking at the graph, because its in the purple shaded region which is where both lines have solutions that are the same. (5,10) is solution to f(x)>1/2x+5 but not a solution to g(x)≤-3x-1. To see if a point is a solution to the system or not you find a point on the graph the plug it in to both inequalities. If the statement is true for one but false for the other then the point is not a solution. If the statement is true for both inequalities then the point IS a solution to the system. 3.5 You want to open your own truck rental company. You do some research and find that the Motor Masters truck rental companies in your area charge a flat fee of $40 plus $0.30 for every mile driven. In your classroom binder, write an equation for the cost of renting a truck from Motor Masters rental company. Also in your classroom binder, create a graphical representation of the cost of renting a truck from Motor Masters. Be sure to label both the x and y-axis in context.
A.) In your wikispace journal, explain what you would need to change about the graph and the equation if you wanted to show the possible costs for a company who was charging LESS than Motor Masters.
B.) You want to charge less for your truck rentals so you can advertise your lower rate and get more business for your company. In your online journal, explain the following:
If you can only change one cost item (either the flat fee OR the mileage fee), which would you change and why? How would this change help your company charge customers less? Remember to think about which change would be better for the customers and which change would be better for your company... even though any change will be better advertising for your company. Be sure to include the new equation that you have chosen to charge with your new adjusted prices.
A.) If I wanted to show possible costs for a company that was charging less than motor masters than I would want to change the flat fee and the amount charged for every mile driven but at the same time keep it at a reasonable price.
B.) If I could only change one then I would change the flat fee and I would change that because its what controls the cost of the rental. If I changed the flat fee I would change it from $40 to $30 because instead of paying $49 with 30 miles driven with Motor Masters they could pay $39 for using 30 miles driven with the other company. The new equation would be y= 0.30x + 30 rather than y= 0.30x + 40.
Graphing Simple Inequalities
After watching the video above on graphing, you need to match the inequality statements below in the document below with their corresponding graphs.
In your wikispace journal, explain your entire thought process (from your first match to your last) and how you narrowed down the choices and knew which graph matched which inequality statement.
Table with answers to the above document is in the document below
To narrow down my choices I looked at the sign of the inequality and determined whether the dot was open or closed then I looked at the point of the inequality which tells me which side to shade the line and I looked at the inequality that had "or" in it which told me that there where no solutions and when there was just and "x" there is solutions.
3.2
Summarize what we did in class today. Explain what similar features are shown in the graph x>5 as you would graph it on a number line and x>5 as you would graph it on a coordinate plane. Also explain the similarities of x<=3 as graphed on a number line and x<=3 on a coordinate plane. Explain how this same thinking applies to y<2x+1 ?? How do you know which side of the line should be shaded since the line is slanted? Be sure to explain the short-cut method as well as the algebraic method you could use to prove that the correct side of the line has been shaded.
x>5 on a number line would have an open circle over 5, going to the right. On a coordinate plane, x>5 would be a dotted line thats shaded above. The open circle on a number line represents a dotted line on a coordinate plane. X≤3 on a number line would have a closed circle above 3 going to the left. On a coordinate plane, x≤3 would have a solid line shaded below. The same thing go with y<2x+1, because is < which means that it will be a dashed line, and shaded below. If its > or
≥, the line is shaded above, and if it's < or ≤, the line is shaded below. To prove which side of the line that has to be shaded, you can pick a point on the coordinate plane from the shaded region, and plug the coordinates into the inequality.
3.3
(Looking at graph on page 113) Write the inequality whose graph is shown. Explain every step of your thinking and how you came up with the inequality.
y≤-1/2+4
First, i looked for the mx+b. I found that the Y intercept was 4, and the slope was -1/2, because it was going down to the right and up to the left. Then, i looked at the kind of line that was shown, and where the shading was. It was a solid line and was shaded below, which meant that it was ≤
3.4
Looking at the shaded graph in the document below, you need to identify a point that is a solution to the system and explain how you know it is a solution by looking at the graph. Also, identify a point that is a solution to only one of the inequalities, but NOT a solution to the system. Explain how you might test a point to determine whether it is a solution to the system or not?
A point that is a solution to the system is (-6,6) I know its a solution by looking at the graph, because its in the purple shaded region which is where both lines have solutions that are the same. (5,10) is solution to f(x)>1/2x+5 but not a solution to g(x)≤-3x-1. To see if a point is a solution to the system or not you find a point on the graph the plug it in to both inequalities. If the statement is true for one but false for the other then the point is not a solution. If the statement is true for both inequalities then the point IS a solution to the system.
3.5
You want to open your own truck rental company. You do some research and find that the Motor Masters truck rental companies in your area charge a flat fee of $40 plus $0.30 for every mile driven. In your classroom binder, write an equation for the cost of renting a truck from Motor Masters rental company. Also in your classroom binder, create a graphical representation of the cost of renting a truck from Motor Masters. Be sure to label both the x and y-axis in context.
A.) In your wikispace journal, explain what you would need to change about the graph and the equation if you wanted to show the possible costs for a company who was charging LESS than Motor Masters.
B.) You want to charge less for your truck rentals so you can advertise your lower rate and get more business for your company. In your online journal, explain the following:
A.) If I wanted to show possible costs for a company that was charging less than motor masters than I would want to change the flat fee and the amount charged for every mile driven but at the same time keep it at a reasonable price.
B.) If I could only change one then I would change the flat fee and I would change that because its what controls the cost of the rental. If I changed the flat fee I would change it from $40 to $30 because instead of paying $49 with 30 miles driven with Motor Masters they could pay $39 for using 30 miles driven with the other company. The new equation would be y= 0.30x + 30 rather than y= 0.30x + 40.